Wien filters are well known and are used as charged-particle beam energy analyzers primarily because they provide high resolution energy analysis of a beam that can be passed straight through the filter. However, use of the filter with charged particle beams has limited applications because of the affect the filter has on the beam.
Generally, a Wien filter is used as an energy analyzer to meet, for example, the following conditions:
(a) To increase the dispersion of particles in a charged particle beam whose energy differs; and PA1 (b) To decrease the dispersion of particles in a charged particle beam having the same energy to effect a convergence action. PA1 (c) To rotate the spin of charged particles in a beam in a predetermined direction; and PA1 (d) To decrease the dispersion of whole particles in a charged particle beam to effect a convergence action.
On the other hand, a Wien filter is used as a spin rotator to meet, for example, the following conditions:
FIG. 2 is a block diagram of a Wien filter illustrating the principle of its operation. Magnetic pole-pieces 101, 102 are arranged opposite to each other, and main electrodes 103, 104 (electric plates) are also arranged opposite to each other. The magnetic field applied by the magnetic pole-pieces 101, 102 and the electric field applied by the main electrodes 103, 104 (in the respective directions of y and x) intersect each other at right angles, whereas the incidence of an electron beam (charged particle beam) is set perpendicular (in the direction of z) to the plane in which the electric and magnetic fields are generated. On condition that the velocity v of charged-particles in the electric field E and the magnetic field B satisfies EQU E=vB (1)
the charged-particle beam moves straight through the filter. If the charged-particles of the beam entering the filter are different in energy or velocity, the condition (1) is not met and the particles do not travel straight, but rather are deflected in the direction of x. Consequently, the particles of a charged particle beam will disperse at the exit of the filter depending on their energy and this satisfies the aforementioned condition (a) of using the filter as an energy analyzer.
On the assumption that the electric field and the magnetic field are uniform in the Wien filter, the beam moves as shown in FIGS. 3(a) and 3(b), wherein the coordinate axes are shown for reference to correspond with the coordinate frame shown in FIG. 2. More specifically, the incident beam is focused in the direction of the electric field E as shown by 34 in FIG. 3(a), but is caused to expand in the filter in proportion to the divergence angle at the time of incidence as shown by 34' in FIG. 3(b) because of the absence of the focusing effect in the direction of the magnetic field B. In other words, an incident electron beam with a circular cross section will have an elliptical cross section as it exits the filter. Therefore, attempts have been made to form such a convergence action because the aforementioned condition (b) is not satisfied thereby.
As previously mentioned, the Wien filter can be used as a spin rotator wherein the spin of charged-particles precesses around the direction of the magnetic field (y-axis). Assuming that the length of the filter extends in the z direction in FIG. 2 and the velocity of the charged-particles are constant in the Wien filter, an angle of rotation of the spin can be regulated in accordance with the intensity of the electric field. The aforementioned condition (c) is satisfied accordingly. However, the condition (d) is not satisfied because the convergence action is not available as in the case of the energy filter.
If the magnetic field and the electric field are so distributed in the Wien filter as expressed by the following equations, charged-particle beams having the same energy are seen to focus stigmatically by solving kinetic equations. EQU Bx=B.times.y/R (2) EQU By=B.times.(1+x/R) (3) EQU Bz=0 (4) EQU Ex=E (5) EQU Ey=0 (6) EQU Ez=0 (7)
where Bx, By, Bz=x, y, z components in the magnetic field B; Ex, Ey, Ez=x, y, z components in the electric field E; B and E are absolute values; R=2mv.sup.2 /E.multidot.e (m=mass of electron, e=electric charge of electron) of the magnetic and electric fields, respectively; the x, y, z coordinates are taken as shown in FIG. 4; and x, y are positions from the origins of the x, y coordinates axes, respectively. As a result, the condition (b) is satisfied, whereas the condition (d) is also met by accelerating the charged-particles immediately before the Wien filter to reduce the dispersion of the relative energy.
FIG. 4 shows an example of a construction providing such an electric and magnetic field. Opposed magnetic pole-pieces 101', 102' each have faces inclined at equal angles with respect to the center line between them. The extrapolated lines along the respective faces of the magnetic pole-pieces are caused to intersect at a point a distance R from the center (point 0 of FIG. 4) of each face. The magnetic field is so inclined as to be expressed by Eqs. (2), (3) and the electric field is made uniform. Thus, an area is created in which the convergence action is exerted (e.g., J. Appl. Phys. Vol. 43, No. 5, p 2,352 (1972), E.times.B Mass Separator Design).